CAT (QA) PYQs

The distance from $B$ to $C$ is thrice that from $A$ to $B$. Two trains travel from $A$ to $C$ via $B$. The speed of train $2$ is double that of train $1$ while traveling from $A$ to $B$ and their speeds are interchanged while traveling from $B$ to $C$. The ratio of the time taken by train $1$ to that taken by train $2$ in travelling from $A$ to $C$ is

A motorbike leaves point $A$ at $1$ pm and moves towards point $B$ at a uniform speed. A car leaves point $B$ at $2$ pm and moves towards point $A$ at a uniform speed which is double that of the motorbike. They meet at $3:40$ pm at a point which is $168 \mathrm{~km}$ away from $A$ . What is the distance, in km, between $A$ and $B$ ?

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by $75\%$. The ratio of the original speed of the motor boat to the speed of the river is